There are several examples of British actors in the US doing American accents. They tend to do them better, IMO, because contrary to what some posters have said, I think a "typical yeehaw" accent done by Brits pretending to be Americans here(think George W's accent rather than the non-rhotic drawl of some areas of the south) wouldn't be something that film and telly directors would let happen. I also think that Stateside it would be noticed more and commented upon by at least some of the audiences. I think that people would ask, "Why does that person sound like a bad imitation of John Wayne/George W/Annie Oakley?"
The husband from Medium (Jake Weber) is British. His accent comes through sometimes with pronunciations. He sounds a bit Canadian at times. He doesn't have "Canadian raising" or anything, but he might say the odd word with the British pronunciation. Gary Oldman does a fairly decent (IMO) American accent when playing American roles. Kate Winslet as well. There are plenty of good examples of Brits using American accents rather well for roles. Personally, I think Hugh Laurie's is okay, but he sounds a bit sing-song and kiddish. A lot of people on American telly do though, and I've begun to wonder if it's a method or a particular coach who has people speak like that to iron out regional accents, both American and from other speakers.
Kim Cattrall (Sam from
Sex and the City is From Liverpool. She lived in Canada a lot. Another "British" actor with a natural accent that's North American is John Barrowman (Captain Jack from Torchwood). He's Scottish, but moved to the States when he was young. They both speak day to day with North American accents. On the (sort of) flip side, Mel Gibson is really American. Yeah, Australian isn't British, but it's always weird when people get shocked to learn that he's not Australian.
When I listen to my old
NPR station (listen to the news one for maximum impact) and the "r"s hurt my ears (to be fair, the Buffalo accent is definitely a subset of Inland North). Some of the people who do American accents on BBC radio have this naturally, but to me, growing up where I did, it doesn't sound like what an American accent sounds like.
To give a good example of an American doing an excellent (IMO) British accent, I think Renee Zellweger did a good job in the "Bridget Jones" films. The only people I've heard criticise it didn't like the idea of an American playing Bridget Jones to begin with.